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  "path": "/abs/2603.19460v1",
  "publishedAt": "2026-03-23T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Tianyu Bell Pan",
    "Damon L. Woodard"
  ],
  "textContent": "**Authors:** Tianyu Bell Pan, Damon L. Woodard\n\nLarge language models (LLMs) demonstrate strong performance, but they often lack transparency. We introduce GeoLAN, a training framework that treats token representations as geometric trajectories and applies stickiness conditions inspired by recent developments related to the Kakeya Conjecture. We have developed two differentiable regularizers, Katz-Tao Convex Wolff (KT-CW) and Katz-Tao Attention (KT-Attn), that promote isotropy and encourage diverse attention. Our experiments with Gemma-3 (1B, 4B, 12B) and Llama-3-8B show that GeoLAN frequently maintains task accuracy while improving geometric metrics and reducing certain fairness biases. These benefits are most significant in mid-sized models. Our findings reveal scale-dependent trade-offs between geometric precision and performance, suggesting that geometry-aware training is a promising approach to enhance mechanistic interpretability.",
  "title": "GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models"
}